The Office of Admissions and Records of a large western university released the
ID: 3150801 • Letter: T
Question
The Office of Admissions and Records of a large western university released the accompanying information concerning the contemplated majors of its freshman class. (Round your answers to three decimal places.)
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(a) What is the probability that a student selected at random from the freshman class is a female?
(b) What is the probability that a business student selected at random from the freshman class is a male?
(c) What is the probability that a female student selected at random from the freshman class is majoring in business?
Choosing
This Major % of Major
That Is
Female % of Major
That Is
Male Business 24 31 69 Humanities 9 58 42 Education 8 68 32 Social science 7 58 42 Natural sciences 5 55 45 Other 47 45
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Explanation / Answer
Following table shows the percentage in decimal format:
(a)
The probability that a student selected at random from the freshman class is a female is
P(female) = 0.24*0.31 + 0.09*0.58 + 0.08*0.68 + 0.07*0.58 + 0.05*0.55 + 0.47*0.45 = 0.0744 + 0.0522 + 0.0544 + 0.0406+0.0275 + 0.2115 = 0.4606
(b)
By the complement rule the required probability is
P(male) = 1 - P(female) = 1 - 0.4606 = 0.5394
(c)
The percentage of female student and majoring in business is
P(female and majoring in business) = 0.24*0.31 = 0.0744
So the probability that a female student selected at random from the freshman class is majoring in business is
P(majoring in business | female ) =P(female and majoring in business) / P(female) = 0.0744 / 0.4606 = 0.1615
Major % of Freshmen % of Major % of Major Choosing That Is That Is This Major Female Male Business 0.24 0.31 0.69 Humanities 0.09 0.58 0.42 Education 0.08 0.68 0.32 Social science 0.07 0.58 0.42 Natural sciences 0.05 0.55 0.45 Other 0.47 0.45 0.55Related Questions
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